1. Introduction
Atmospheric rivers (ARs) play a vital role in delivering rain and snow to western North America (Ralph et al. 2004; Leung and Qian 2009; Guan et al. 2010; Ralph et al. 2010; Dettinger et al. 2011; Neiman et al. 2013). In some regions, as much as 50% of annual precipitation falls on days when an AR is present (Rutz et al. 2014). ARs play an important role in regional recovery from drought (Dettinger 2013) and have been linked to major flooding events in western North America and elsewhere (Ralph et al. 2006; Neiman et al. 2008, 2011; Lavers et al. 2011; Moore et al. 2012). Despite the importance of ARs to water supply and flood risk, the precipitation resulting from ARs remains poorly forecast (Ralph et al. 2010; Junker et al. 2009; Wick et al. 2013b; Lavers et al. 2016). The processes that cause AR precipitation include cloud microphysics (submeter scales), surface moisture fluxes (from submeter to mesoscales), orographic uplift by terrain (from a few kilometers to synoptic scales), and fluid dynamical processes. The latter can operate on the mesoscale (e.g., narrow cold frontal rainbands; Browning and Roberts 1996), synoptic, and global scales. Regardless of the numerical weather prediction (NWP) model one chooses to create a precipitation forecast, some of these scales will not be resolved.
Global numerical weather prediction (GNWP) models, those that can explicitly simulate the largest weather scales on Earth, can also explicitly resolve the scales of mesoscale fluid dynamic features, but do not explicitly resolve the smallest orographic uplift, surface flux, or cloud microphysics scales. To explicitly resolve finer spatial scales, the weather prediction community has traditionally employed regional numerical weather prediction (RNWP) models to dynamically downscale GNWP forecasts [e.g., the National Oceanographic and Atmospheric Administration (NOAA) North American and High-Resolution Rapid Refresh models (Weygandt et al. 2009), the Deutscher Wetterdienst Consortium for Small-Scale Modeling (Baldauf et al. 2011)]. The RNWP models explicitly resolve finer scales without the aid of empirical parameterization, but most operational weather prediction systems that rely upon RNWP are still unable to explicitly resolve the finest scales (cloud microphysics, surface fluxes, small-scale terrain variability) important to landfalling AR precipitation. In the near future, numerical techniques that allow consistent solutions of the fluid dynamics equations across computational grids with multiple or adjustable resolutions promise to “unify” global and very fine scales in numerical weather prediction [e.g., Model Prediction Across Scales (Skamarock et al. 2012), NOAA’s Next Generation Global Prediction System (Michalakes et al. 2015)]. Even with this advance, NWP models will retain an effective limit to explicit spatial resolution that will lie somewhere between scales of topographic variability and fine turbulence scales. We note that while several authors have measured NWP model error for ARs (Junker et al. 2009; Ralph et al. 2010; Kim et al. 2013; Wick et al. 2013b; Swain et al. 2015; Lavers et al. 2016), the predictability limit—the time beyond which it is no longer possible to predict the state of a system, given knowledge of current and past states, with a desired level of accuracy (American Meteorological Society 2017)—for NWP forecasts of AR and their related atmospheric fields has not been established. Additionally, it is not known whether RNWP may improve upon the predictability limit.
Ralph et al. (2013a, hereafter R13) presented a useful way to apportion the impacts of scale-dependent processes on precipitation. The authors used a long record of observations at an atmospheric river observatory (ARO; White et al. 2009, 2013) to demonstrate that the amount of orographic precipitation is linearly related to the bulk upslope flux (BUF) of atmospheric water vapor content by the horizontal wind in a lower tropospheric layer (see their Fig. 5). It has been demonstrated that BUF is also a skillful predictor of instantaneous precipitation rate (Neiman et al. 2002, 2009). Other authors have similarly found that orographic precipitation amount is related to the rate of water vapor flux directed normal to the terrain (Alpert 1986; Barros and Lettenmaier 1994; Sinclair 1994; Colle 2004; Smith and Barstad 2004; Barstad and Smith 2005). These studies examined many regions other than northern coastal California; thus, the importance of low-level moisture flux and the linear relationship found by R13 is applicable to midlatitude orographic precipitation in general.
R13 and Neiman et al. (2009) convincingly demonstrated that the orographic precipitation response to the forcing (vapor transport at approximately low-level jet height) upon a mountain range applied by an AR is linear to first order. If the predictability limit and predictive skill during an AR can be improved, will this lead to more accurate precipitation prediction? An important step in demonstrating this for any modeling system will be to demonstrate that the modeled orographic precipitation response is correct. This precipitation response is somewhat scale dependent, though discussion in Neiman et al. (2002, 2009), White et al. (2009), Smith et al. (2010), and Kingsmill et al. (2013) demonstrates that the horizon between the forcing scale and the response scale is not identical. Nonetheless, a large part of the simulated forcing response relies upon high-resolution terrain, and we thus expect this to improve with higher-resolution modeling systems.
In the current study, we intend to meet the following goals by analyzing forecasts made by two separate models, a GNWP [the Global Forecast System reforecasts (GFSRe; Hamill et al. 2013)] and an RNWP [the Weather Research and Forecast (WRF) Model (Skamarock 2008)]:
Characterize the predictability limit of atmospheric state and structure near and within ARs in the midlatitude northeast Pacific Ocean (approximately between latitudes 25° and 45°N). To do so, we will examine the dependence of errors on forecast lead times that are as great as 7 days.
Measure errors in the simulated orographic forcing–response relationship during landfalling ARs.
Comment on the suitability of RNWP for forecasting precipitation during ARs and use the lessons learned from goals 1 and 2 to suggest model improvements that are most likely to improve precipitation forecasts during landfalling ARs.
The remainder of this manuscript will be organized as follows. The GFSRe, WRF, and verification datasets used will be described in section 2. Analysis methods, including the method of apportioning precipitation error by scale, will be described in section 3. Section 4 will present the results of the verification analyses, and section 5 will summarize results and suggest improvements in NWP that may lead to better precipitation forecasts during landfalling ARs.
2. Data and forecast models
a. Atmospheric river observatory
The California Department of Water Resources (DWR) operates an ARO comprising two individual stations, Bodega Bay (BBY) and Cazadero (CZC) in California, as part of the Enhanced Flood Response and Emergency Preparedness (EFREP) network (White et al. 2009, 2013). The BBY station is situated on the coast at sea level and is designed to monitor horizontal vapor flux, integrated water vapor (IWV), and horizontal winds in the atmospheric river low-level jet (LLJ) as it impinges upon the orographically productive coastal mountain ranges. The CZC station is located north of Bodega Bay at the top of a prominent ridge. The CZC station reports precipitation, vertical S-band radar reflectivity, and precipitation drop size distributions during AR conditions. By adapting the techniques of R13, we will use the couplet of stations to investigate orographic forcing (hereafter “forcing”) near the coastal edge of the Russian River Watershed (RRW) through bulk upslope flux measured at BBY and orographic precipitation response (hereafter “response”) via accumulated precipitation measured at CZC.
BUF is calculated following the methods of Neiman et al. (2002, 2009), in which the controlling layer (800–1200 m MSL) winds are multiplied by the local IWV and projected onto the mountain orthogonal direction. Controlling layer wind is calculated from the 449-MHz wind profiler at BBY. IWV is calculated via radio occultation from the BBY GPS Trimble receiver. Rainfall accumulation at CZC is measured by a tipping-bucket rain gauge and reported to 0.1-mm precision. Hourly, quality-controlled BUF and accumulated rainfall are available from the NOAA Earth System Research Laboratory via anonymous ftp server.
b. GPS-enabled soundings
Airborne dropsondes from the CalWater 2 early start (CWES) and CalWater 2015 (CW2) intensive observing periods (Ralph et al. 2016) are used extensively in our analyses of forecast skill and predictability limit. Each sounding occurred during a midlatitude northeast Pacific AR transect performed by CalWater aircraft. An example, with two transects used in this study, is shown in Fig. 1. Transects were executed to maintain a flight path perpendicular to the direction of troposphere integrated water vapor flux, and 179 sondes from 15 transects taken during 10 separate AR flights are used in this study (Table 1). Herein, an AR is only considered for analysis if maximum integrated vapor transport (IVT; Cordeira et al. 2013) exceeds 500 kg m−1 s−1 by direct observation or by ARO proxy (see section 2c). This threshold will herein be referred to as the “moderate AR” threshold. It reflects the minimum IVT typically leading to significant precipitation upon landfall by a northeast Pacific AR and has emerged through discussions during the first International Conference on Atmospheric Rivers (Ralph et al. 2017). We require a dropsonde transect to cross the full width of the AR core. Herein, the AR core boundaries are defined by the isopleth where IVT exceeds 500 kg m−1 s−1. If the transect includes dropsondes that recorded IVT ≥ 500 kg m−1 s−1 and at least one poleward and one equatorward dropsonde that recorded IVT < 500 kg m−1 s−1, then the transect is considered to have sampled the full AR core. Last, transect terminal dropsondes must be greater than 100 km from the WRF lateral boundaries to reduce the chance that imprecise advection closure or the boundary damping layer impact the forecast soundings. Soundings were used to estimate AR environment variables: 500-hPa geopotential height 
ERA-Interim reanalysis IWV for 1200 UTC 8 Feb 2014. Overlaid are the dropsondes from two aircraft transects during CalWater early start campaign IOP 2. Individual dropsonde locations are depicted by white circles and numbered in chronological order. These correspond to OCN cases CWES 2 and CWES 3 from Table 1. The text box summarizes some impacts of this AR described in Ralph et al. (2016). Black boxes “a” and “b” correspond to domain boundaries for WRF 9 km and WRF 3 km, respectively.
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
OCN cases simulated for this study. More information regarding IOPs and aircraft can be found in Ralph et al. (2016).
c. Forecast periods
We simulated two groups of ARs occurring between December 2014 and March 2016. These simulations became the forecast datasets that were used to evaluate the GFSRe and WRF predictability limits and to measure errors in the simulated orographic forcing–response relationship for each model. The first group, OCN (for oceanic AR events), included 15 moderate ARs in the midlatitude northeast Pacific Ocean for which GPS-enabled dropsondes were available during a CalWater transect (see Table 1). The OCN airborne observations represent a rich survey of the vertical and transport-normal structures of oceanic AR. The OCN cases were therefore used to investigate the ability of GFSRe and WRF to accurately simulate the transport-normal structure of orographic forcing (e.g., vertical distribution of vapor transport and moist static stability) at forecast lead times up to 7 days.
Many of the ARs in the OCN cases did not cause significant precipitation over land, so a second group of forecast periods [LND (for landfalling AR events); see Table 2] was chosen to investigate GFSRe and WRF quantitative precipitation forecast (QPF) skill and apportionment of QPF error among scales during moderate ARs impacting the RRW. LND AR cases were chosen using the following criteria:
The ARO must have recorded AR conditions following R13 for 24 or more hours.
During AR conditions at the ARO, IVT must have exceeded 500 kg m−1 s−1, or BUF must have exceeded 300 mm m s−1. The latter has been found to be a proxy for moderate AR conditions.
The 10 strongest ARs by storm-integrated BUF that occurred between 1 December 2014 and 31 March 2016 and met criteria 1 and 2 were grouped into the LND case list.
LND cases simulated in this study.
d. GEFS reforecasts
The National Centers for Environmental Prediction (NCEP) Global Ensemble Forecast System (GEFS) model serves as the GNWP for the tests presented herein. We required that all forecast periods used the same deterministic model. To satisfy this requirement, we acquired control member forecasts from the NOAA Global Ensemble Reforecast Dataset (Hamill et al. 2013). GFSRe forecasts are initialized once per day at 0000 UTC and run to 192 h lead time. GFSRe serves as the WRF parent model in this study. The GFSRe dataset is produced with GEFS version 9.0.1, run at approximately 40-km native resolution. Since 15 January 2015, NOAA has run an updated GFS deterministic forecast with a native resolution of approximately 13 km. Because the majority of the OCN case skill calculations require forecasts initialized before this date, we did not choose the higher-resolution deterministic GFS for the primary GNWP in this study. We have run parallel simulations where possible using the deterministic GFS to verify that key results do not change significantly given the higher-resolution GNWP. The analyses created from these parallel simulations can be found in the online supplemental material. Methods of generating WRF from the higher-resolution GNWP (GFS 0.25; see supplemental material) and methods of postanalysis are identical to those presented herein.
e. WRF
The open-source WRF-ARW model (Skamarock 2008) is used in this study. We configured WRF with two domains utilizing horizontal resolutions of 9 and 3 km (hereafter WRF 9 km and WRF 3 km, respectively). Both WRF 9 km and WRF 3 km are configured with 60 vertical levels with compressed spacing near the 925- and 300-hPa levels in a U.S. Standard Atmosphere sounding. Static land surface information for WRF simulations is generated from the USGS land-use database (Wang et al. 2012) at a resolution of 5 (2) arc-min for WRF 9 km (3 km). WRF domains and parameterized physics options are listed in Table 3. The domains, vertical spacing, and nesting ratio were chosen based on sensitivity tests using the dropsondes from the OCN case list to measure forecast performance in IVT. Parameterized physics options were chosen according to author experience and common practice in other WRF NWP forecast efforts. We stress that the WRF parameterized physics used herein have not been objectively optimized.
Domain attributes and parameterized physics options for WRF configurations in this study.
The WRF 9 km domain has a much larger Earth-relative footprint (Fig. 1, box “a”) and utilizes interpolated forecasts from GFSRe as boundary conditions. Initial conditions for both WRF domains are interpolated from the GFSRe analysis to the WRF 9 km and WRF 3 km grids using the WRF preprocessor (Wang et al. 2012). The WRF 3 km domain Earth-relative footprint (Fig. 1, box “b”) covers most of the state of California and portions of western Nevada and southern Oregon. The RRW, where precipitation is verified in this study, lies near the center of the 3-km domain. The WRF domain configurations described here are also used to create operational forecasts at the Center for Western Weather and Water Extremes (CW3E; http://cw3e.ucsd.edu/). The CW3E operational model, named West-WRF, has the primary goal of predicting extreme precipitation events (especially those associated with ARs) that are key to water supply and flooding in the region (Dettinger et al. 2011; Ralph and Dettinger 2012; R13). As they are further developed, West-WRF operational forecasts will be oriented to the special requirements posed by western U.S. extreme precipitation. These requirements were summarized recently in a study carried out in support of the Western States Water Council’s request for a vision for future observational needs for extreme precipitation monitoring, prediction, and climate trend detection (Ralph et al. 2014). This summary built upon more than a dozen reports from various agencies and science groups over the previous few years and on experience in developing California’s unique observing network (White et al. 2013) and from NOAA’s Hydrometeorology Testbed (Ralph et al. 2013b). In addition to operational forecast goals, West-WRF is designed as a platform from which to evaluate the sources of forecast error and their relationship to physical processes.
3. Methods
a. The verification matrix procedure
The predictability limit (goal 1 in the introduction) has been estimated from a number of forecasts with systematically varying lead time. These forecasts are generated using the verification matrix procedure, described thusly. To estimate the skill for a single event at n lead times, one needs n forecasts that verify at the time of event 
b. Estimates of predictive skill
For AR environment variables, we define the predictive skill of each model’s forecast as the Brier skill score (BSS; Winterfeldt et al. 2011) using GFSRe climatology (1991–2015, December–March) as the reference forecast. The BSS is equivalent to measuring the fractional reduction in error variance by the more accurate forecast. The predictability limit in any AR environment variable is considered to be reached when BSS ≤ 0. GFSRe climatology is not available at full vertical resolution, and therefore it is not feasible to estimate the model climatology for the AR core variables. Instead, the predictability limit is crossed for dIVT and 
Qualitative and quantitative methods are used to assess accuracy in QPF for the models considered. We compute histograms from each model’s QPF for each lead time in the three lead-time verification bins and compare to histograms computed from the NCEP Stage IV ST QPE. The population is drawn from all events and all Stage IV grid points within the RRW. For quantitative measures, we calculate the mean, standard deviation, and root-mean-square of the quantity QPF − QPE at all NCEP Stage IV grid points and for all models and lead times as appropriate. Bilinear interpolation is used to transform QPF on the WRF 3 km and GFSRe grids to the NCEP Stage IV grid.
c. Linearization of the forcing and response relationships, reduction in error
We also assess whether reducing error in the forcing or reducing error in the simulated response, independent of forcing, leads to a larger reduction of error in the forecast ST Pr.
(a) ST Pr and ST BUF at the ARO for 171 historical rain events (dark gray dots) and the linear trend line resulting from a least squares fit (red line). The correlation coefficient 
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
d. Sonde data processing
Each dropsonde is processed by vertical smoothing onto isobaric surfaces every 25 hPa from 1000 to 300 hPa. The diagnostic variables calculated include IVT, moist Brunt–Väisälä frequency 
Two of the 15 total transect observing periods required unique processing. Those are transect 1 on 7 February 2014 and transect 4 on 11 February 2014. Both of these transects are a composite of two spatially offset flight tracks.
e. Transect compositing procedure
To derive AR-normal composite cross sections, it was necessary to align the dynamical features within each AR transect. First, each individual dropsonde is linearly interpolated to a gridded AR-normal transect with a resolution of 50 km. Second, a common center among the transects is defined as the dropsonde with maximum IVT and the endpoints defined by most poleward and equatorward sondes. Finally, a composite of the transects is created by taking the arithmetic mean of the interpolated transects.
f. NWP forecast to observation interpolation
1) Spatial interpolation to sondes and temporal interpolation
Forecasts from GFSRe and WRF 9 km have been spatially interpolated from their native grids to the dropsonde Earth-relative location using a bilinear method. There are two sources of temporal uncertainty in our methods. First, no attempt has been made to temporally interpolate NWP output to sonde report time. To create composite dropsonde transects, we must assume stationarity in the AR up to the longest time between transect start and end. This time is 2 h and 27 min, or very near the 3-h output interval for each model. Second, the GFSRe duty cycle is 24 h, but the valid time of any given observation may occur anywhere in the diurnal cycle. The sources of temporal uncertainty above lead primarily to random temporal imprecision in model to observation matching, though we cannot rule out that these sources of temporal imprecision will accumulate to nonzero residual. Because their temporal offset is likely to be much larger than the time a dropsonde takes to profile the atmosphere below flight level, no effort is made to account for the sonde drift in the forecast interpolation. The location used is the mean of the individual sonde latitude and longitude reports.
2) Atmospheric river observatory
NWP forecast output from all models was bilinearly interpolated to both ARO locations. Model output was also linearly interpolated from the model native coordinate to the effective retrieval heights (m AGL) of the 449-MHz wind profiling radar.
3) NCEP Stage IV QPE
Model output was bilinearly interpolated from native grids to the locations of the NCEP Stage IV QPE product. Model output was masked thereafter to exclude any points lying outside the boundaries of the RRW. Watershed boundaries were defined by a georeferenced shapefile created by the USGS. Masking by the shapefile polygon was performed using NCAR Command Language version 6.2 (http://www.ncl.ucar.edu/).
4. Results
a. Predictability limit in AR state variables
GFSRe predictive skill for lead times 24–144 h is displayed in Fig. 3a. BSS is estimated for 
(a) Value added by GFSRe over GFSRe climatology validated against 145 CalWater 2 dropsondes for the state variables 
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
For 
The value added by WRF 9 km to GFSRe for the first six lead times considered is displayed in Fig. 3c. From Fig. 3c it is apparent that WRF 9 km adds value to GFSRe for AR state variables between 36 h 
We recreated the analysis in Fig. 3 using GFS 0.25 as the GNWP and West-WRF 9 km. This companion analysis is shown in the supplemental material as Fig. S3. When the parent model is GFS 0.25, WRF 9 km adds value for 84 h 
b. Vertical structures of AR static stability
We investigated the predictive skill in forecasts of moist static stability by GFSRe and WRF 9 km from the sample of dropsondes for which IVT ≥ 500 kg m−1 s−1. This analysis is shown in Fig. 4 using the normalized mean-square error and bias in forecast moist Brunt–Väisälä frequency 
(top) Normalized mean-square error [Eq. (2)] in 
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
(top) OCN case mean AR normal–vertical transect of dIVT error (model minus observation; kg m−1 s−1; color fill), and 
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
c. Vertical structures of AR core horizontal vapor transport
Figure 5a displays the composite AR cross sections of dIVT from the OCN case AR core transects. The methodology for constructing each cross section is discussed in section 3f. The center panel in Fig. 5 displays the observed composite. In this panel, there is a strong local maximum in water vapor flux near 900 hPa located at the analyzed AR core center. This water vapor flux maximum is located just below a weak composite LLJ (isotach composite, not shown). Equivalent potential temperature isotherms in Fig. 5 show the composite AR core straddling a baroclinic zone with temperatures decreasing poleward of the core center. This composite structure is consistent with AR cross sections reported in Cordeira et al. (2013) and Ralph et al. (2016).
The remaining panels in Fig. 5 display the mean dIVT error (forecast minus observed) composite in WRF and GFSRe for the three lead-time verification bins. Overlaid in each is the composite forecast 
d. Deterministic QPF skill during landfalling AR
Value histograms for WRF 3 km and GFSRe ST QPF at NCEP Stage IV grid points within the RRW for the three lead-time verification bins are shown in Fig. 6. Figure 6 also displays the LND case ST QPE histogram. ST QPE from the cases investigated had median and upper (lower) quartile values of 61 and 97 (41) mm. For short lead times (Fig. 6a), the WRF 3 km QPF histogram most closely resembles the QPE histogram. The inset tables in Fig. 6 display mean QPF − QPE (Bias), the standard deviation of QPF − QPE (σ), and the root-mean-square error (RMSE) QPF − QPE for both WRF 3 km and GFSRe. Both WRF 3 km and GFSRe produce low-biased ST QPF across lead times. For 
(a) Value histogram for RRW ST QPE (NCEP Stage IV; green bars), WRF (blue x), and GFSRe (red +). ST QPF calculated from 12 h 
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
For 
Analysis from Fig. 6 does not definitively answer whether WRF 3 km or GFSRe QPF is more accurate for RRW landfalling AR. Neither WRF 3 km nor GFSRe distinguished itself in a large or consistent manner over the lead times considered. Thus far, we have seen that the WRF and GFSRe systems display minor strengths relative to each other in AR state, structure, and RRW QPF, but on balance perform with similar accuracy. However, we cannot simply assume that the QPF performance result follows from the predictive skill in dIVT and static stability. Each model may arrive at its simulated precipitation uninformed by the correct orographic forcing–response relationship. If so, we cannot expect improvements in model forcing accuracy (e.g., improvements in the skill from Figs. 4 and 5) to lead to improvements in precipitation skill.
e. Relationships between orographic forcing and response
To adequately address the second goal posed in the introduction, we must investigate each model’s ability to accurately reproduce the observed forcing–response relationship during an AR. To this end, we turn to the 10-yr record of bulk upslope vapor flux and mountaintop precipitation collected at the ARO. Figure 7a shows the observed, GFSRe simulated, and WRF 3 km simulated ST BUF–ST Pr relationship for 60 h 
(a) ST Pr and ST BUF at the ARO for all LND observed (colored circles), GFSRe forecasts (colored asterisk), and WRF forecasts (colored circle and cross) with lead times 60 h 
Citation: Journal of Hydrometeorology 19, 7; 10.1175/JHM-D-17-0098.1
Measures of error for ST storm-scale forcing and local-scale response, as well as reduction of error in response by prescribing linearized ARO observed forcing and response to GFSRe and WRF LND case forecasts.
From Fig. 7a and Table 5 we conclude that WRF 3 km better predicts the multifactor orographic forcing–response at the ARO. We are also interested in asking the following questions of both models: do errors in ST Pr during ARs arise primarily due to errors in forcing or in the response, and which model may benefit from adjustments to accuracy in either forcing or the response relationship? To investigate this, we present 
To interpret the 
WRF 
In contrast, GFSRe 
We also recreated the analyses in Fig. 7 and Table 5 using GFS 0.25 and the companion WRF 3 km forecasts using GFS 0.25 as initial and boundary conditions. These analyses can be found in Fig. S7 and Table S6, respectively. The broad results from the above section apply when comparing GFS 0.25 to its downscaled WRF forecasts: WRF reduces 
5. Discussion
This study is the first to investigate predictability limit of AR state and AR core variables by GNWP and RNWP and to relate deficiencies in those to AR precipitation skill by measuring the error in the simulated orographic forcing–response relationship. It was found that WRF 9 km is capable of adding value to its parent GNWP by means of dynamical downscaling for a subset of medium-range weather prediction time scales. This result suggests that assimilation of observations into the coarse domain at model native scales may additionally improve forecasts created by WRF 9 km.
Generally, WRF 9 km and GFSRe forecasts of AR vertical and transport-normal structures were found to reproduce realistic vapor transport in the LLJ region of ARs at short lead times, but forecasts of LLJ water vapor flux were found to develop significant low bias by 
WRF 3 km and GFSRe displayed similar accuracy in predicting RRW storm-total precipitation during the AR considered. As lead time increased, both models produced a significant dry bias compared to the observed accumulated precipitation distribution. This finding may follow from the inability of both models to produce a strong AR LLJ at longer lead times (Fig. 5). The authors note that tuning of the parameterized physics submodels in WRF for the purpose of accurately predicting AR precipitation has not been done and that QPF smoothed to lower resolutions (e.g., the difference in resolution between WRF 3 km and GFSRe) has been shown to result in higher skill scores over complex terrain (Mass et al. 2002).
When predicting storm-total precipitation at a mountaintop well known to be orographically productive (CZC), WRF improves upon GFSRe mean-square error by as much as 69% at short lead times. It appears that this improvement occurs primarily because WRF better reproduces the relationship between orographic forcing (approximated by ST BUF) and response (ST Pr at CZC). This can be seen visually in Figs. 7a and 7b and quantitatively in Table 5. WRF 3 km very accurately reproduces the ST BUF–ST Pr relationship found through observations during the AR cases studied.
It is found that improvement in WRF QPF can be expected through either more accurate forcing (e.g., data assimilation) or response (e.g., parameterized physics tuning). WRF forcing at the ARO was often low-biased, in agreement with the low-bias in LLJ dIVT (Fig. 7). Thus, the consistent underprediction of RRW ST Pr (Fig. 6) is partially caused by storm-scale forcing that is too weak. This cause-and-effect relationship cannot be verified for GFSRe, since ST BUF errors from GFSRe are more randomly distributed (Fig. 7b) and since the local response relationship is not similar to that observed.
The analysis presented herein suggests that improvements to either forcing or orographic precipitation response will straightforwardly lead to more accurate precipitation in WRF or similar RNWP. This is true even at lead times approaching 7 days. Therefore, WRF may be an attractive option to produce skillful QPF for regions in which heavy rain events are dominated by atmospheric rivers, especially given intensive work to develop data assimilation techniques to address the low bias found in LLJ water vapor flux and to develop more accurate parameterizations of key subgrid-scale processes such as surface energy fluxes and cloud microphysics.
Acknowledgments
The U.S. Army Corps of Engineers Award W912HZ-15-SOI-0019, the National Science Foundation XSEDE Award ATM150010, and the California Department of Water Resources provided financial support for this research. The authors would also like to thank the NOAA CalWater airborne science teams, the NOAA Physical Science Division’s Hydrometeorological Testbed, and the University of California, Davis, Bodega Marine Laboratory for providing data and facilities. Additionally, the authors thank Scripps Institution of Oceanography for establishing the Center for Western Weather and Water Extremes.
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